Hybrid model for the analysis of the modal properties of a ball screw vibration system

In accordance with the vibration characteristics of ball screw feed systems, a hybrid modeling method is proposed to study its dynamic behavior. Partially, the ball screw is modeled as a continuous body, and the remaining components are considered lumped masses, allowing for a realistic description of the dynamics of the feed system. The axial, torsional, transverse, and bending vibration models of a ball screw carriage system are established via the Rayleigh-Ritz series method based on the Timoshenko beam assumption. The established model that added the Timoshenko beam assumption obtains the coupling vibration displacement between the transverse and bending vibrations of the lead screw, which is close to real situations. Numerical simulations are conducted to investigate the changes of the natural frequency and modal shapes of ball screw systems with carriage positions. Results show that the carriage position has significant influence on the amplitude and direction of axial and transverse vibrations, substantial influence on the direction of the bending vibration, and minimal influence on the amplitude and direction of torsional vibration. These results indicate that the proposed hybrid model performs well to predict the vibration characteristics of the feed system. Moreover, the carriage position and carriage load also have a remarkable effect on the frequency response of the feed system. These results, along with the modeling approach, provide an important basis for the further study of in-machining monitoring and vibration controller design.